Finite Group DatabasebetaFinite Group Databasebeta| order | 5760 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 786432 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C4×C5×C16 |
| multiplicative | (ℤ/6851)ˣ, (ℤ/7259)ˣ, (ℤ/8435)ˣ, (ℤ/9333)ˣ, (ℤ/9399)ˣ, (ℤ/10845)ˣ, (ℤ/12532)ˣ, (ℤ/13702)ˣ, (ℤ/14518)ˣ, (ℤ/16870)ˣ, (ℤ/18666)ˣ, (ℤ/18798)ˣ, (ℤ/21690)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
5760 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.